Comparing Strategies for DNS Based Optimization of Airfoils for Martian Rotorcraft

Abstract

Martian atmospheric conditions present various challenges when designing rotorcraft. Specifically, the thin atmosphere and lower speed of sound compared to Earth requires Martian rotor blades to operate in a low-Reynoldsnumber ( approximately equal to 103 to 104) compressible regime, for which conventional airfoils have not been designed. Airfoils with sharp leading edges and flat surfaces have been shown to perform better than conventional airfoils under these conditions. In order to find the optimal airfoils, several studies have explored optimizing non-conventional airfoils with evolutionary techniques. These algorithms usually require many cost function evaluations, and hence, they typically employ Reynolds-Averaged Navier Stokes (RANS) solvers because of their low computational cost. However, RANS solvers have limited predictive capability when the flow becomes unsteady and separated at moderate angles of attack. Enabled by recent advances in solver technology and GPU hardware, we are able to overcome this limitation by undertaking optimization using high-fidelity Direct Numerical Simulations (DNS), able to capture the flow physics, via the compressible flow solver in PyFR (www.pyfr.org). In order to reduce the cost of the optimization, given that it involves expensive cost function evaluations, the current study compares two multi-objective optimization strategies using pymoo (www.pymoo.org) as the optimizer. Specifically, the study compares the cost of Genetic Algorithm (GA) optimization with two-dimensional DNS used to evaluate the cost function, with the cost of surrogate-assisted GA optimization where the model is generated and updated with two-dimensional DNS. Results help elucidate efficient strategies for high-fidelity two- and three-dimensional DNS optimization for aerospace applications, specifically rotorcraft airfoils in Martian atmospheric conditions.